SOLUTION: please help--I've tried this for 2 days. Solve {{{0=9x^2+24x+10}}} using the quadratic formula.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: please help--I've tried this for 2 days. Solve {{{0=9x^2+24x+10}}} using the quadratic formula.      Log On


   



Question 315740: please help--I've tried this for 2 days.
Solve 0=9x%5E2%2B24x%2B10 using the quadratic formula.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

0=9x%5E2%2B24x%2B10

9x%5E2%2B24x%2B10=0

Compare to

ax%5E2%2Bbx%2Bc=0 and find that

a=9, b=24, and c=10

Then substitute in

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

x+=+%28-24+%2B-+sqrt%28+24%5E2-4%2A9%2A10+%29%29%2F%282%2A9%29+ 

x+=+%28-24+%2B-+sqrt%28+576-360+%29%29%2F18+

x+=+%28-24+%2B-+sqrt%28216+%29%29%2F18+

216 is not a perfect square. However it has a perfect square
36 as a factor for 36*6 is 216. So we write 36*6 instead of 216

x+=+%28-24+%2B-+sqrt%2836%2A6%29%29%2F18+

Now to take the square root of the product 36*6 by taking individual 
square roots of 36 and 6

x+=+%28-24+%2B-+sqrt%2836%29sqrt%286%29%29%2F18+

Now we know the square root of 36 is 6, so we write 6 instead of sqrt%2836%29.

x+=+%28-24+%2B-+6sqrt%286%29%29%2F18+

Next we factor 6 out of the top:

x+=+%286%28-4+%2B-+sqrt%286%29%29%29%2F18+

Finally we cancel the 6 in the top into the 18 in the bottom 

x+=+%28cross%286%29%28-4+%2B-+sqrt%286%29%29%29%2Fcross%2818%29%5B3%5D+

That leaves 3 in the bottom:

x+=+%28-4+%2B-+sqrt%286%29%29%2F3+

Edwin